A predictive method allowing the use of a single ionic model in
numerical cardiac electrophysiology

M. Rioux and Y. Bourgault

Department of Mathematics and Statistics, University of
Ottawa, Canada
ybourg@uottawa.ca

Received:
5
January
2012

Abstract

One of the current debate about simulating the electrical activity in the heart is the
following: Using a realistic anatomical setting, i.e. realistic
geometries, fibres orientations, etc., is it enough to use a simplified 2-variable
phenomenological model to reproduce the main characteristics of the cardiac action
potential propagation, and in what sense is it sufficient? Using a combination of
dimensional and asymptotic analysis, together with the well-known Mitchell − Schaeffer
model, it is shown that it is possible to accurately control (at least locally) the
solution while spatial propagation is involved. In particular, we reduce the set of
parameters by writing the bidomain model in a new nondimensional form. The parameters of
the bidomain model with Mitchell − Schaeffer ion kinetics are then set and shown to be in
one-to-one relation with the main characteristics of the four phases of a propagated
action potential. Explicit relations are derived using a combination of asymptotic methods
and ansatz. These relations are tested against numerical results. We illustrate how these
relations can be used to recover the time/space scales and speed of the action potential
in various regions of the heart.

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